Problem of the Week

Updated at Sep 29, 2014 8:32 AM

How can we solve for the derivative of \({x}^{2}+{e}^{x}\)?

Below is the solution.



\[\frac{d}{dx} {x}^{2}+{e}^{x}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} {x}^{2})+(\frac{d}{dx} {e}^{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[2x+(\frac{d}{dx} {e}^{x})\]

3
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[2x+{e}^{x}\]

Done
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